The present invention relates to the field of resistivity measurement of semiconductor surfaces.
In the prior art, the variation of resistivity as a function of temperature in semiconductors was either ignored or a particular value for the thermal coefficient of resistivity was assumed. The thermal coefficient of resistivity, or the ratio of the change in resistivity over a 1.degree. C. temperature change, is small for bulk silicon or unprocessed silicon wafers. Typical values are .+-.1%/.degree. C., i.e. the resistivity of the wafer surface varies up to 1 percent over a 1.degree. C. variation of the temperature at the wafer surface. Since a 1% variation is such a small change, the thermal coefficient of resistivity is often ignored. Ignoring the coefficient is equivalent to using a value of 0%/.degree. C. for the thermal coefficient of resistivity, resulting in an error in a resistivity reading of about .+-.1% for each 1.degree. C. of thermal drift during the measurement process. In many applications, such an error might be insignificant, however as the demands placed on semiconductors for ever smaller and faster circuits, such errors become very problematic.
Where the thermal coefficient of resistivity is not ignored, a value for the coefficient is often selected from a table of coefficients for silicon wafers having various dopant concentrations. While this may result in suitable coefficient approximations for unprocessed silicon, the thermal coefficient of resistivity for a patterned thin film layer on the surface of a wafer cannot be easily determined by reference to a table. Furthermore, this would yield only a crude approximation, since many more characteristics of a wafer affect the value of the coefficient than can be accounted for in any table of a reasonable size. Thus, in many other applications where the thermal coefficient of resistivity is not ignored, the accuracy of a table coefficient is sufficient. Nonetheless, some applications require even more accuracy.
Semiconductor wafers with high dopant concentrations will have lower resistivities, so in terms of absolute resistivity, a percentage error in a resistivity measurement causes a small error in the absolute resistivity, and a resistivity measurement ignoring the thermal variation might be in error by only a small percentage. However, as resistivity increases, the absolute error increases, as for example, when the dopant concentration is lowered. When two high resistivity areas of the wafer must be matched, as in analog resistor pair matching, the absolute error is more important than the percentage variation. For example, on a wafer with two matched areas of approximately 50 M.OMEGA./square, ignoring the thermal coefficient of resistivity can result in an error of as much as 50 K.OMEGA./square in the differential resistivity between the areas.
From the above it is seen that an improved method and apparatus for measuring resistivity to account for the thermal coefficient of resistivity are needed.